# Maximum with Lagrange multiplier

I am trying to find the maximum of f(x,y)=(x+y)4+y4f(x,y)=(x+y)^4+y^4 constrained to x4+y4=1x^4+y^4=1.

Using Lagrange Multiplier I get
(x+y)3=λx3
(x+y)^3=\lambda x^3

(x+y)3+y3=λy3
(x+y)^3+y^3=\lambda y^3

But I don’t see how to proceed after this.

Do you have some idea on this problem ?

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1

Is f(x,y)=x+y4+y4=x+2y4f(x,y)=x+y^4+y^4=x+2y^4 right or do you have a typo ?
– callculus
2 days ago

Thank you. I have corrected the formula.
– Spout
2 days ago

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